Question 1006203: Compare the intensity of an earthquake that measures 6.0 on the Richter scale to the intensity of an earthquake that measures 4.0 on the Richter scale by finding the ratio of the larger intensity to the smaller intensity.
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Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! this can get real complicated, so i'll try to make it as simple as possible while ignoring the complexity of what's behind all the measurements.
the formula for the richter scale is R = log10(An/S) where S is an earthquake with a standard intensity that is used as the base for the measurement.
consequently, you get 2 measurements.
6 = log10(A6/S)
4 = log10(A4/S)
by the basic definition of logarithms, you get:
6 = log10(A6/S) if and only if 10^6 = A6/S
4 = log10(A4/S) if and only if 10^4 = A4/S
solve for A6 and you get A6 = 10^6 * S
solve for A4 and you get A4 = 10^4 * S
the ratio of A6 to A4 is equal to A6 / A4.
you get A6/A4 = (10^6 * S) / (10^4 * S) which becomes:
A6/A4 = (10^6 / 10^4) * (S / S) which becomes:
A6/A4 = 10^2 = 100.
what this says is that an earthquake that measures 6 on the richter scale has an intensity that is 100 times the intensity of an earthquake that measures 4 on the richter scale.
in general, an increase of 1 on the richter scale means an intensity that is 10 times greater.
an increase of 2 is 100 times greater.
an increase of 3 is 1000 times greater, etc.
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